No ifs, ands or buts about it,
1) The slabs are too thick to dry in a short time. Those slabs look to be at least 4" thick, will take 2 years to air dry. You can pay to kiln dry them, if the kiln has accommodations for such small quantity of wood. Kiln drying will likely not prevent checking.
2) Even slow air drying, those slabs will check..... and the bark is likely to slough off.
You can try finishing just the top surface with a water based finish, like Varethane Crystal Floor finish. This finish might adhere satisfactorily to the "dampened" wood surface. By not finishing the bottom surface, you'd be allowing the drying process to occur through the unfinished bottom-side. After some good time (years), the table(s) might be ready for a refinishing of the whole, anyway, then you can apply a finish to the bottom side.
As to epoxy, West System's G-Flex 650-8 is a two part epoxy that is applicable in or under water. The problem with this epoxy is, it's opaque or doesn't have the clear coat finish properties you seem to want, West System might have a clear coating epoxy that is applicable to wet surfaces. I use the GF 650 for adhesive purposes, so I haven't looked or needed the other. Give West Systems a call, click the "need help tab". There's a product guide, there, also. https://www.westsystem.com/
*You'll be hard pressed to maintain the bark on those slabs, no matter how you attempt to keep it on.
A note about logs, drying, milling, etc. .... I've dealt with logging and these sorts of projects for a long time. Ever drive by a logging company, where hundreds/thousands of logs are piled out in their yard? The logs are subjected to a sprinkling system, keep them wet..... plus an insecticide. This sprinkler system prevents checking and bug infestations, until the logs are milled. You might want to cut your slabs in *half, then submerge them for a few months, then air dry them and periodically wetting them. You don't want them to air dry fast. As to kiln drying, ask the folks at the kiln about drying slabs as that. I don't dry my slabs using a kiln, so I don''t know their technique, if there's one, to prevent checking.
*Half size slabs will be plenty sturdy and definitely won't be so heavy. Those slabs are, no doubt, heavy as heck. The whole table a real bear of heaviness..... need a forklift to move it? Green oak is about 50+ lbs per cubic foot... not much less when dry. Cut in half, you can make 2 tables or 1 table and a couple of side tables. Or a cutting block or 2, for the kitchen.
Live oak, aye? Where abouts are you located, Louisiana perhaps?